Sr Examen
Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
- Integrales paso a paso
- Ecuaciones diferenciales paso a paso
- Límites paso por paso
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¿Cómo usar?
- Derivada de:
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Derivada de e^x*sin(x)
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Derivada de x*e^(1/x)
- Derivada de x!
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Derivada de e^y
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Expresiones idénticas
- y=e^(arctg^ dos √(2x- uno))
- y es igual a e en el grado (arctg al cuadrado √(2x menos 1))
- y es igual a e en el grado (arctg en el grado dos √(2x menos uno))
- y=e(arctg2√(2x-1))
- y=earctg2√2x-1
- y=e^(arctg²√(2x-1))
- y=e en el grado (arctg en el grado 2√(2x-1))
- y=e^arctg^2√2x-1
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Expresiones semejantes
- y=e^(arctg^2√(2x+1))
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Expresiones con funciones
- arctg
- arctg(sqrt(x))
- arctg^2(1/x)
- arctg(cos(x))
- arctg(x+cosx)
Derivada de y=e^(arctg^2√(2x-1))
Solución
Ha introducido
[src]
2 _________ atan (x)*\/ 2*x - 1 E
$$e^{\sqrt{2 x - 1} \operatorname{atan}^{2}{\left(x \right)}}$$
E^(atan(x)^2*sqrt(2*x - 1))
Primera derivada
[src]
/ 2 _________ \ 2 _________ | atan (x) 2*\/ 2*x - 1 *atan(x)| atan (x)*\/ 2*x - 1 |----------- + ---------------------|*e | _________ 2 | \\/ 2*x - 1 1 + x /
$$\left(\frac{2 \sqrt{2 x - 1} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{\sqrt{2 x - 1}}\right) e^{\sqrt{2 x - 1} \operatorname{atan}^{2}{\left(x \right)}}$$
Segunda derivada
[src]
/ 2 \ |/ __________\ 2 __________ __________ | __________ 2 || atan(x) 2*\/ -1 + 2*x | 2 atan (x) 2*\/ -1 + 2*x 4*atan(x) 4*x*\/ -1 + 2*x *atan(x)| \/ -1 + 2*x *atan (x) ||------------ + --------------| *atan (x) - ------------- + -------------- + --------------------- - ------------------------|*e || __________ 2 | 3/2 2 / 2\ __________ 2 | |\\/ -1 + 2*x 1 + x / (-1 + 2*x) / 2\ \1 + x /*\/ -1 + 2*x / 2\ | \ \1 + x / \1 + x / /
$$\left(- \frac{4 x \sqrt{2 x - 1} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{2 \sqrt{2 x - 1}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 \sqrt{2 x - 1}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{2 x - 1}}\right)^{2} \operatorname{atan}^{2}{\left(x \right)} + \frac{4 \operatorname{atan}{\left(x \right)}}{\sqrt{2 x - 1} \left(x^{2} + 1\right)} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{\left(2 x - 1\right)^{\frac{3}{2}}}\right) e^{\sqrt{2 x - 1} \operatorname{atan}^{2}{\left(x \right)}}$$
Tercera derivada
[src]
/ 3 \ |/ __________\ 2 __________ __________ / __________\ / 2 __________ __________ \ 2 __________ | __________ 2 || atan(x) 2*\/ -1 + 2*x | 3 3*atan (x) 6 12*x*\/ -1 + 2*x 6*atan(x) 4*\/ -1 + 2*x *atan(x) | atan(x) 2*\/ -1 + 2*x | | atan (x) 2*\/ -1 + 2*x 4*atan(x) 4*x*\/ -1 + 2*x *atan(x)| 12*x*atan(x) 16*x *\/ -1 + 2*x *atan(x)| \/ -1 + 2*x *atan (x) ||------------ + --------------| *atan (x) + ------------- + ---------------------- - ----------------- - ---------------------- - ---------------------- - 3*|------------ + --------------|*|------------- - -------------- - --------------------- + ------------------------|*atan(x) - ---------------------- + --------------------------|*e || __________ 2 | 5/2 2 3 / 2\ 3/2 2 | __________ 2 | | 3/2 2 / 2\ __________ 2 | 2 3 | |\\/ -1 + 2*x 1 + x / (-1 + 2*x) / 2\ __________ / 2\ \1 + x /*(-1 + 2*x) / 2\ \\/ -1 + 2*x 1 + x / |(-1 + 2*x) / 2\ \1 + x /*\/ -1 + 2*x / 2\ | / 2\ __________ / 2\ | \ \1 + x / *\/ -1 + 2*x \1 + x / \1 + x / \ \1 + x / \1 + x / / \1 + x / *\/ -1 + 2*x \1 + x / /
$$\left(\frac{16 x^{2} \sqrt{2 x - 1} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{12 x \sqrt{2 x - 1}}{\left(x^{2} + 1\right)^{3}} - \frac{12 x \operatorname{atan}{\left(x \right)}}{\sqrt{2 x - 1} \left(x^{2} + 1\right)^{2}} - \frac{4 \sqrt{2 x - 1} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 \sqrt{2 x - 1}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{2 x - 1}}\right)^{3} \operatorname{atan}^{3}{\left(x \right)} - 3 \left(\frac{2 \sqrt{2 x - 1}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{2 x - 1}}\right) \left(\frac{4 x \sqrt{2 x - 1} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{2 \sqrt{2 x - 1}}{\left(x^{2} + 1\right)^{2}} - \frac{4 \operatorname{atan}{\left(x \right)}}{\sqrt{2 x - 1} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{\left(2 x - 1\right)^{\frac{3}{2}}}\right) \operatorname{atan}{\left(x \right)} + \frac{6}{\sqrt{2 x - 1} \left(x^{2} + 1\right)^{2}} - \frac{6 \operatorname{atan}{\left(x \right)}}{\left(2 x - 1\right)^{\frac{3}{2}} \left(x^{2} + 1\right)} + \frac{3 \operatorname{atan}^{2}{\left(x \right)}}{\left(2 x - 1\right)^{\frac{5}{2}}}\right) e^{\sqrt{2 x - 1} \operatorname{atan}^{2}{\left(x \right)}}$$
Gráfico